So my question:
Is mic in the same as line in, when I turn off plug in power?
No. Mic Power only affects the Mic In port by feeding a small amount of electricity to power a condenser microphone. The recorder is expecting much more signal to come from the device when it is plugged into Line In.
Here's how SHURE, the microphone, pre-amp, mixer etc. company's engineers explain the difference between Mic Levels and Line Levels:
"Mic-level or microphone-level signal is the amount of voltage that comes out of a microphone when someone speaks into it - just a few ten-thousandths of a volt. (Of course, this voltage varies somewhat in response to changes in speaking volume and source-to-mic distance.)
A line-level signal is approximately one volt, or about 10,000 times as strong as a mic-level signal, so the two do not ordinarily use the same input.Connecting a microphone to a line-level input will result in almost no sound at all, because the signal is so faint that the line input cannot hear it.
Connecting a line-level source (such as a CD player) to a mic-level input will cause the sound to be loud and distorted because the line signal is much stronger than what the mic input will accept.
Microphone level is usually specified between -60 and -40 dBu. Line level is considered to be +4 dBu"
Hope that helps.
Having said all that, you should be getting a signal when you plug a CD player or any "Line Out" source into "Line In" on the H2. You may, indeed, have a problem with your unit.
But a battery box does not equal a pre-amplifier. If you use a battery box, you still use "Mic In."